Which of the following terms is responsible for noise measurement in the PID controller?

Proportional + Derivate:

The additive combination of proportional & Derivative control is known as P-D control.

The overall transfer function for a PD controller is given by:

\({G_C}\left( s \right) = \frac{{U\left( s \right)}}{{E\left( s \right)}} = {K_P} + s{K_D}\)

PD controller is nothing but a differentiator (or) a High Pass Filter.

The frequency of noise is very high. So this high pass filter will allow noise into the system which results in noise amplification.

Effects of Proportional Derivative (PD) controllers:

• Decreases the type of the system by one
• Reduces the rise time and settling time
• Rise time and settling time decreases and Bandwidth increases
• The speed of response is increased i.e. the transient response is improved
• Improves gain margin, phase margin, and resonant peak
• Increases the input noise
• Improves the stability

Effects of Proportional Integral (PI) controllers:

• Increases the type of the system by one
• Rise time and settling time increase and Bandwidth decreases
• The speed of response decreased i.e. transient response becomes slower
• Decreases the steady-state error and steady-state response is improved
• Decreases the stability